Mysterious negative sign required sometimes #105

[ElMapacheDelOeste]

The rotations returned by the function axis_rotation() are the transposed to the ones we expected. Using Modelica for reference, the same function returns the transpose to the Julia's ones :
https://github.com/modelica/ModelicaStandardLibrary/blob/afba9aad9216b472b856b259a002c934b46e6786/Modelica/Mechanics/MultiBody/Frames/axisRotation.mo#L12

This allows to get rid of the suspicious need for the "neg_w" boolean.

I have a doubt for the quaternions, if the transpose is only needed on the rotation matrix or on the angular velocity as weel.

GitHub issue : #105

[ElMapacheDelOeste]

Should the transpose be done on the RotationMatrix(R,w) and therefore have -w as well?

[baggepinnen]

Thanks for this PR! I'll try to have a look at it when we have the new compiler up and running :)

[pitx-perf]

Jumping in since I worked with @ElMapacheDelOeste on this.
It's worth mentioning that before this PR, the convention of angles did not match Modelica - I think this is important to point out because people benchmarking the package could get confused and dismiss it.

See the test "resistance in speherical" for instance:
. the Revolute is rotated as expected because it uses a (correct) planar_rotation under the hood
. the Spherical is rotated by the opposite of the angle, because it uses the faulty axes_rotations function. But compensate by a "-" in the translation.